The combined average weight of an okapi and a llama is $450$ kilograms. The average weight of $3$ llamas is $190$ kilograms more than the average weight of one okapi. On average, how much does an okapi weigh, and how much does a llama weigh? On average, an okapi weighs
Solution: Let $x$ represent the average weight of an okapi and let $y$ represent the average weight of a llama. Since we have two unknowns, we need two equations to find them. Let's use the given information in order to write two equations containing $x$ and $y$. For instance, we are given that the combined average weight of an okapi and a llama is $\textit{450}$ kilograms. How can we model this sentence algebraically? Since their combined average weight is $450$ kilograms, we get the following equation: $ x+ y = 450$ We are also given that the average weight of $\textit{3}$ llamas is $\textit{190}$ kilograms more than the average weight of one okapi. This can be expressed as: $x +190 = 3y$ Let's rewrite this equation so that it's solved for $x$ : $x = 3y-190$ Now that we have a system of two equations, we can go ahead and solve it! Let's substitute $ x={3 y-190}$ into the first equation: $\begin{aligned} x+y &= 450\\\\ ({3y-190})+y&=450\\\\ 4y &=640\\\\ y&=160\end{aligned}$ Now we can substitute $y = 160$ into $x+y=450$ and find that $x=290$. Recall that $x$ denotes the average weight of an okapi and $y$ denotes the average weight of a llama. Therefore, an okapi weighs $\textit{290}$ kilograms on average and a llama weighs $\textit{160}$ kilograms on average.